So the discussion has come up as to if casement windows and vertical operators (single hungs and double hungs) look alike.

There's no easy way to say no they don't but it's okay.  That is my take on it though.

Here are some examples:

This is a double casement.  Both sides swing out for ventilation.  The outside has a very flat beveled look to it with what's designed to look like a putty glazed, 45 degree angle to the glass.

This is the NT Window Presidential Vinyl Replacement Window.  It has a cove moulding look to the outside profile that sticks out past the face of the window frame.

This is a close up of the casement window.

Again this is a casement seen in the above shot.

This is a single hung archtop with a profile that is almost the opposite of the casement on close examination.